Investigation of excess environmental risk around putative sources: Stone's test with covariate adjustment

Stone (Statistics in Medicine, 7, 649-660 (1988)) proposed a method of test ing for elevation of disease risk around a point source. Stone's test is ap propriate to data consisting of counts of the numbers of cases, Y-i say, in each of n regions which can be ordered in increasing distance from a point source. The test assumes that the Y-i are mutually independent Poisson var iates, with means mu(i) = E(i)lambda(i) where the E-i are the expected numb ers of cases, for example based on appropriately standardized national inci dence rates, and the lambda(i) are relative risks. The null hypothesis that the lambda(i) are constant is then tested against the alternative that the y are monotone non-increasing with distance from the source. We propose an extension to Stone's test which allows for covariate adjustment via a log-l inear model, mu(i) = E(i)lambda(i) exp(Sigma(j=1)(p) x(ij)beta(j)), where t he x(ij) are the values of each of p explanatory variables in each of the n regions, and the beta(j) are unknown regression parameters. Our methods ar e illustrated using data on the incidence of stomach cancer near two munici pal incinerators. Copyright (C) 1999 John Wiley & Sons, Ltd.